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A geometric formalism is developed which allows to describe the non-linear regime of higher-spin gravity emerging on a cosmological quantum space-time in the IKKT matrix model. The vacuum solutions are Ricci-flat up to an effective vacuum…
Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the…
We discuss the reconstruction of generic 3+1-dimensional space-time geometries from covariant quantum spaces as backgrounds in the IKKT matrix model. An explicit recipe to realize generic classical geometries is provided. Even though this…
We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin…
We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find…
We present a systematic study of spherically symmetric vacuum solutions of the IKKT matrix model, within the framework of semi-classical covariant quantum geometries. All asymptotically flat solutions of the equations of motion of the frame…
A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…
We derive the full set of field equations based on Hossenfelder's recent covariant formulation of the emergent gravity model, along with perturbative and exact solutions. The exact solution describes a static, spherically-symmetric…
Homogeneous time-dependent solutions of massive gravity generalise the plane wave solutions of the linearised Fierz-Pauli equations for a massive spin-two particle, as well as the Kasner solutions of General Relativity. We show that they…
A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action,…
We show that the gravitational field equations derived from an action composed of i) an arbitrary function of the scalar curvature and other scalar fields plus ii) connection-independent kinetic and source terms, are identical whether one…
The Polynomial Affine Gravity is an alternative gravitational model, where the interactions are mediated solely by the affine connection, instead of the metric tensor. In this paper, we explore the space of solutions to the field equations…
The torsion is shown to be vitally important in the explanation of the evolution of the universe in a large class of gravitational theories containing quadratic terms of curvature and torsion. The cosmological solutions with homogeneous and…
In this paper, we provide a vacuum solution with torsion in quadratic Riemann-curvature gravity. Physically, the solution means that vacuum can have a nonzero vacuum field with large torsion. We show that the Einstein-Hilbert action can be…
Dilaton gravity with general brane localized interactions is investigated. Models with corrections up to arbitrary order in field derivatives are considered. Effective gravitational equations of motion at the brane are derived in the…
We consider general $k=-1$ FLRW covariant quantum spacetimes $\mathcal{M}^{3,1} \times \mathcal{K}$ with fuzzy extra dimensions $\mathcal{K}$ as classical solutions of the IKKT matrix model. The coupled equations of motion are recast in…
We write the field equations of torsion gravity theories and the N\oe ther identity they obey directly in terms of metric and contorsion tensor components expressed with respect to natural coordinates, i.e. without using vierbien but…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…